Finally, let us define the dark matter content that we will use in our analysis. As in [1]}, [2]}, we will adopt simple but well-motivated dark matter density profiles with respect to the \(\Lambda \) CDM scenario. Compilations of observations from galaxies and their agglomerates, supported by numerical simulations [3]}, [4]}, [5]}, suggest that the dark matter halo can be described by the Navarro-Frenk-White (NFW) density profile, whose analytical expression is defined as
\(\rho =\rho _{NFW}=\frac{\rho _s}{\frac{r}{R_s}\left(1+\frac{r}{R_s}\right)^2},\) 
